Problem: Solve for $x$ and $y$ using elimination. ${2x-y = 19}$ ${-3x+y = -29}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-x = -10$ $\dfrac{-x}{{-1}} = \dfrac{-10}{{-1}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {2x-y = 19}\thinspace$ to find $y$ ${2}{(10)}{ - y = 19}$ $20-y = 19$ $20{-20} - y = 19{-20}$ $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ You can also plug ${x = 10}$ into $\thinspace {-3x+y = -29}\thinspace$ and get the same answer for $y$ : ${-3}{(10)}{ + y = -29}$ ${y = 1}$